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Research Papers

A Nonisothermal PEM Fuel Cell Model Including Two Water Transport Mechanisms in the Membrane

[+] Author and Article Information
K. Steinkamp

 Fraunhofer Institute for Solar Energy Systems, Heidenhofstrasse 2, 79110 Freiburg, Germanykay@ise.fhg.de

J. O. Schumacher

 Institute for Computational Physics, Zuercher Hochschule Winterthur, P.O. Box 805, CH-8401 Winterthur, Switzerlandscr@zhwin.ch

F. Goldsmith

 Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139cfgold@mit.edu

M. Ohlberger

Institute for Applied Mathematics, Albert-Ludwigs-Universitaet Freiburg, Herrmann Herderstrasse 10, 79110 Freiburg, Germanymario@mathematik.uni-freiburg.de

C. Ziegler

 Fraunhofer Institute for Solar Energy Systems, Heidenhofstrasse 2, 79110 Freiburg, Germanycziegler@ise.fhg.de

J. Fuel Cell Sci. Technol 5(1), 011007 (Jan 16, 2008) (16 pages) doi:10.1115/1.2822884 History: Received July 13, 2007; Revised September 25, 2007; Published January 16, 2008

A dynamic two-phase flow model for proton exchange membrane fuel cells is presented. The two-dimensional model includes the two-phase flow of water (gaseous and liquid) in the gas diffusion layers (GDLs) and in the catalyst layers (CLs), as well as the transport of the species in the gas phase. The membrane model describes water transport in a perfluorinated-sulfonic-acid-ionomer-based membrane. Two transport modes of water in the membrane are considered, and appropriate coupling conditions to the porous CLs are formulated. Water transport through the membrane in the vapor equilibrated transport mode is described by a Grotthus mechanism, which is included as a macroscopic diffusion process. The driving force for water transport in the liquid equilibrated mode is due to a gradient in the hydraulic water pressure. Moreover, electro-osmotic drag of water is accounted for. The discretization of the resulting flow equations is done by a mixed finite element approach. Based on this method, the transport equations for the species in each phase are discretized by a finite volume scheme. The coupled mixed finite element/finite volume approach gives the spatially resolved water and gas saturation and the species concentrations. In order to describe the charge transport in the fuel cell, the Poisson equations for the electrons and protons are solved by using Galerkin finite element schemes. The electrochemical reactions in the catalyst layer are modeled with a simple Tafel approach via source/sink terms in the Poisson equations and in the mass balance equations. Heat transport is modeled in the GDLs, the CLs, and the membrane. Heat transport through the solid, liquid, and gas phases is included in the GDLs and the CLs. Heat transport in the membrane is described in the solid and liquid phases. Both heat conduction and heat convection are included in the model.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Layer assembly of a PEM fuel cell. Five layers of a PEM fuel cell are modeled: cathodic GDL, anodic GDL, cathodic CL, anodic CL, and membrane. The two gas channels are taken into account as boundary conditions into the model.

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Figure 2

Plot of the capillary pressure as a function of the liquid water saturation pc(sw) according to the Brooks–Corey model. The GDLs are hydrophobic, and therefore the capillary pressure is negative. The intersection point with the y axis denotes the threshold pressure pd.

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Figure 3

The two transport modes of water in the membrane are illustrated (25). (1) For λ⩽2, the membrane is nearly impermeable for water. (2) Vapor equilibrated transport mode: For 0⩽λ⩽14, a network of inverted micelles (drawn as circles) arises around the sulfonic acid groups of Nafion. Water molecules can be transported through this network by building H3O+ ions together with protons. This transport of hydrated protons through the membrane is described by the Grotthus mechanism and can be modeled macroscopically like a diffusion (26). (3) Liquid equilibrated transport mode: For 14⩽λ⩽22, more and more connections between the micelles are expanded to channels, which are filled with liquid water. A coherent liquid phase with well-defined hydraulic pressure is formed. The fraction of already expanded channels in a considered volume is labeled with S.

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Figure 4

Coupling diagram of the PEM fuel cell model. The transport mechanisms and the solution variables (state variables) of the corresponding PDEs are written in the boxes. Each arrow indicates a coupling between two PDEs, the coupling state variables that are contained in the PDEs are noted at the arrows.

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Figure 5

The model domain is shown. R1–R4 indicate boundaries between subdomains. The solid lines correspond to the outer boundaries RI–RIII.

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Figure 6

The grid geometry used for simulations. The figure shows the five layers of the fuel cell.

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Figure 7

Distribution of the liquid water saturation sw at different points in time. (a) The evaporation process is already visible after 0.001s. (b) and (c) show further progression of the evaporation process. Due to the boundary conditions, a residual saturation remains at the left and right outer boundaries. In the membrane, the liquid water saturation is not defined, and thus its value there is arbitrary and with no relevance to the simulation.

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Figure 8

The mass fraction cH2 of hydrogen after 0.03s and 0.10s. Due to the electrochemical reaction, a depletion of hydrogen in the anodic CL can be observed. (a) and (b) show the spatial dissolved distributions of cH2. In (c), the hydrogen mass fraction is displayed along a cross section through the anodic GDLs and CLs.

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Figure 9

The mass fraction cO2 of oxygen after 0.03s and 0.10s. Due to the electrochemical reaction, a depletion of oxygen in the cathodic CL can be observed. (a) and (b) show the spatial dissolved distributions of cO2. In (c), the oxygen mass fraction is displayed along a cross section through the cathodic GDLs and CLs.

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Figure 10

The mass fraction cH2O of water vapor neglecting phase transitions. In (a)–(c), the spatial distributions of cH2Ov are shown at three different times, 0.005s, 0.030s, and 0.100s. Water vapor is produced in the cathodic CL as a result of the oxygen reduction reaction. Additionally, water vapor is transported through the membrane as can be seen by the water vapor depletion on the anode side. (d) shows the water vapor mass fraction along a cross section through the cell.

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Figure 11

The temperature distribution after 0.024s and 0.090s is shown. As can be seen in (a) and (b), the main heat source is located in the cathodic CL. This is due to the exothermal reaction occurring there. (c) shows the respective cross sections of the temperature distribution through the cell.

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